Facet-inducing web and antiweb inequalities for the graph coloring polytope

For a graph GG and its complement Ḡ, we define the graph coloring polytope P(G)P(G) to be the convex hull of the incidence vectors of star partitions of Ḡ. We examine inequalities whose support graphs are webs and antiwebs appearing as induced subgraphs in GG. We show that for an antiweb W̄ in GG the corresponding inequality is facet-inducing for P(G)P(G) if and only if W̄ is critical with respect to vertex colorings. An analogous result is also proved for the web inequalities.